Rapidly rotating black holes in dynamical Chern-Simons gravity: Decoupling limit solutions and breakdown

Rapidly rotating black holes are a prime arena for understanding corrections to Einstein's theory of general relativity (GR). We construct solutions for rapidly rotating black holes in dynamical Chern-Simons (dCS) gravity, a useful and motivated example of a post-GR correction. We treat dCS as an effective theory and thus work in the decoupling limit, where we apply a perturbation scheme using the Kerr metric as the background solution. Using the solutions to the scalar field and the trace of the metric perturbation, we determine the regime of validity of our perturbative approach. We find that the maximal spin limit may be divergent, and the decoupling limit is strongly restricted for rapid rotation. Rapidly-rotating stellar-mass BHs can potentially be used to place strong bounds on the coupling parameter $\ell$ of dCS. In order for the black hole observed in GRO J1655-40 to be within the decoupling limit we need $\ell \lesssim 22$ km, a value 7 orders of magnitude smaller than present Solar System bounds on dynamical Chern-Simons gravity.